Abstract
The Janis-Newman-Winicour metric is a solution of Einstein’s gravity minimally coupled to a real massless scalar field. The γ-metric is instead a vacuum solution of Einstein’s gravity. Both spacetimes have no horizon and possess a naked singularity at a finite value of the radial coordinate, where curvature invariants diverge and the spacetimes are geodetically incomplete. In this paper, we reconsider these solutions in the framework of conformal gravity and we show that it is possible to solve the spacetime singularities with a suitable choice of the conformal factor. Now curvature invariants remain finite over the whole spacetime. Massive particles never reach the previous singular surface and massless particles can never do it with a finite value of their affine parameter. Our results support the conjecture according to which conformal gravity can fix the singularity problem that plagues Einstein’s gravity.
Highlights
The Janis-Newman-Winicour metric is a solution of Einstein’s gravity minimally coupled to a real massless scalar field
The γ-metric is instead a vacuum solution of Einstein’s gravity. Both spacetimes have no horizon and possess a naked singularity at a finite value of the radial coordinate, where curvature invariants diverge and the spacetimes are geodetically incomplete. We reconsider these solutions in the framework of conformal gravity and we show that it is possible to solve the spacetime singularities with a suitable choice of the conformal factor
Massive particles never reach the previous singular surface and massless particles can never do it with a finite value of their affine parameter
Summary
The JNW spacetime is an exact solution of the Einstein equations in which matter is described by a real massless scalar field φ. For μ = 1, the JNW metric has a naked singularity at the radial coordinate rsing = M (μ − 1). The γ-metric is an exact solution of the vacuum Einstein equations [19, 20, 23]. It belongs to the class of the Weyl metrics. For γ = 1, the spacetime is spherically symmetric and we recover the Schwarzschild solution. For γ = 1, the spacetime has a naked singularity at the radial coordinate rsing = 2M.
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